Details

sample549.0ms

Algorithm

intervals

Results

79.0ms	26×	body	1280	nan
59.0ms	277×	body	80	nan
40.0ms	169×	body	80	valid
35.0ms	31×	body	1280	valid
23.0ms	25×	body	640	valid
22.0ms	23×	body	640	nan
11.0ms	16×	body	320	valid
8.0ms	12×	body	320	nan
6.0ms	15×	body	160	valid
3.0ms	6×	body	160	nan

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
7	3812
6	1805
5	729
4	393
3	181
2	93
1	42
0	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.5b	(* (sqrt 2) t)
11.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
24.0b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

49.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
13.0ms	(* (sqrt 2) t)
362.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
57.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
76.0ms	(* (sqrt 2) t)
288.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify5.0s

Counts

96 → 96

Iterations

Iter	Nodes
3	8442
2	1582
1	441
0	170

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* t t) (/ (* l l) x))
4.8b	(/ (* l l) x)
6.0b	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
29.6b	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-*l/` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `sum-log` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 66

Calls

4 calls:

9.0ms	(+ (* t t) (/ (* l l) x))
18.0ms	(/ (* l l) x)
37.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
18.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* t t) (/ (* l l) x))
22.0ms	(/ (* l l) x)
110.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4))
340.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (* (/ t (/ x t)) 4)))

simplify3.5s

Counts

78 → 78

Iterations

Iter	Nodes
3	7421
2	1496
1	424
0	151

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2) t)
1.0b	(+ (* t t) (/ l (/ x l)))
6.0b	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
29.6b	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-l/` `add-cube-cbrt` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `insert-posit16`
3×	`associate-r`
2×	`+-commutative` `sum-log` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 67

Calls

4 calls:

16.0ms	(* (sqrt 2) t)
21.0ms	(+ (* t t) (/ l (/ x l)))
23.0ms	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
27.0ms	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sqrt 2) t)
53.0ms	(+ (* t t) (/ l (/ x l)))
118.0ms	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
373.0ms	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

simplify3.0s

Counts

79 → 79

Iterations

Iter	Nodes
3	5947
2	1306
1	392
0	145

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
1.0b	(+ (* t t) (/ l (/ x l)))
6.0b	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
29.6b	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`pow1`
9×	`add-sqr-sqrt` `add-cbrt-cube` `associate-l` `add-exp-log`
8×	`-un-lft-identity` `associate-l/` `add-cube-cbrt` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `insert-posit16`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 69

Calls

4 calls:

26.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
12.0ms	(+ (* t t) (/ l (/ x l)))
26.0ms	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
50.0ms	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
42.0ms	(+ (* t t) (/ l (/ x l)))
75.0ms	(+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4))
278.0ms	(sqrt (+ (* (+ (* t t) (/ l (/ x l))) 2) (* (/ t (/ x t)) 4)))

simplify3.3s

Counts

81 → 81

Iterations

Iter	Nodes
3	6372
2	1420
1	423
0	151

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

regimes960.0ms

Accuracy

76.7% (5.4b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 27.3b

bsearch1.4s

Steps

Iters	Range		Point
8	6.023070278966295e+69	2.1098351165430223e+73	3.525018208516232e+71
10	1.2089538548914101e-204	2.8866228226668404e-186	6.060995535621362e-188
8	9.129779142213335e-256	1.0029032142203589e-252	5.314962770796106e-253
8	-1.0009127210867583e+61	-7.1872129094663955e+56	-8.830678604357355e+59

simplify34.0ms

Iterations

Iter	Nodes
2	73
1	73
0	56

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.2s	10114×	body	80	nan
1.2s	1037×	body	640	valid
1.1s	5043×	body	80	valid
986.0ms	898×	body	1280	valid
647.0ms	388×	body	160	valid
640.0ms	314×	body	320	nan
579.0ms	563×	body	1280	nan
486.0ms	634×	body	320	valid
433.0ms	578×	body	640	nan
68.0ms	200×	body	160	nan